FURTHER SPECULATION ON OCTAGONAL SYMMETRY

by Gerald Huth on February 9, 2011

I have noted on numerous occasions that this spatial nano-antenna explanation of the vision process opens entirely new avenues for thought and have pointed out an increasing number of these. A current development reported in SCIENCE NEWS  Engineers Grow Nanolasers on Silicon, Pave Way for on-Chip Photonics would seem to present one such avenue.

One might go on to read the complete NATURE PHOTONICS  on-line paper “Nanolasers grown on silicon” referenced in the above release.

The authors emphasize in this solid state effort the challenge of growing expansion mismatched materials adjacent to one another. The basic point here, however, is the nano-pillar structure that is grown and the dimensional similarity – nanometer diameter and micron length –  to the biological receptors of the retina.

What first struck me was the following figure from the news release (but does not appear in the NATURE PHOTONICS paper):

The octagonal symmetry jumps out at you – although the authors seem to be attempting to “hexagonalize” the motif.  From the figure, note the octagonal white “surrounding aura” emanating from what appear as eight individual nano-pillars (although two of the elements – top and bottom – are of smaller dimensions than the other six).

To remind – this nano-antenna explanation for light interaction with the retina finds that the octagonal motif of rods-around-cones at 7-8 degrees of retinal eccentricity geometrically defines the exact mid band point of the visual band and, further, that this octagonal motif seems to be present in the distribution of visual receptors in seemingly all (?) species.

I had thought initially that the figure represented the laser emission quoted by the authors and that this emission emanated from an octagonal arrangement of individual 300 nanometer (their measurement) pillars. This turns out as becomes clear in the NATURE PHOTONICS paper not to be the case. The authors believe that laser emission represents an emission from a single subwavelength nano-pillar. Now, this may be the case but I just do not understand it (and beg to be illuminated). Their quote: “Whereas traditional Fabry–Perot modes are inhibited by the interface between InGaAs and silicon, helical modes can strongly localize light within nanopillars of even subwavelength dimensions…”

I must add, importantly, I had not realized until reading the full paper that the above figure represents a simulation and not actual laser emission as I had first assumed.

As I have  previously written in  OPTICAL LIGHTGUIDES HAVING DIAMETER SMALLER THAN THE WAVELENGTH OF LIGHT, it has recently been found ( Tong et al, “Single-mode guiding properties of subwavelength silica and silicon wire waveguides” , OPTICS EXPRESS, Vol.12, No.6, 22 March 2004) that when a fiberoptic lightguide is reduced in diameter to dimensions less than light wavelength (i.e., less than ~0.5 micron or 500 nm), instead of being transmitted through the interior of the guide, light flows around (or on the “outside of”) the guide itself. A further finding was that the more the diameter of the guide is reduced the more light flows outside.

Quoting a popularized description of this finding from a Nanotechnology website:

“Silica Nanowires Thinner Than The Wavelength of Light”

“Marrying fiber optics with nanotechnology, scientists at Harvard University have created silica wires that are far narrower than the wavelength of light yet can still guide a light beam with great precision. The wires, about a thousandth the width of a human hair, function with minimal signal loss even when their walls accommodate well under half the breadth of a single light pulse. A team led by Harvard’s Eric Mazur and Limin Tong, a visiting professor from Zhejiang University in China, reports the work in the Dec. 18 issue of the journal Nature. “You wouldn’t normally imagine that a baseball could pass through a garden hose, but these nanowires appear able to handle exactly that kind of wide load,” says Mazur, Harvard College Professor, Gordon McKay Professor of Applied Physics and professor of physics. “In some cases light is propagating along wires just one-third the width of its own wavelength. It’s almost as if the wire serves as a rail to guide the light rather than funneling it in the traditional sense.” The nanowires carry light via evanescent waves that envelop the slender filaments. If two of the wires touch, light can jump directly from one to the other, something that’s not possible with conventional fiber optics. Although as thin as 50 nanometers, the wires created by Mazur and Tong are up to two centimeters long, making them faintly visible to the naked eye. They display impressive resilience and flexibility, curling easily into light-conducting loops whose diameter is just a tiny fraction of a millimeter.

I have proposed that this finding provides a fundamental basis for this nano-antenna explanation of light interaction with the external-to-the-lightguide evanescent wave forming the necessary connection between adjacent receptors.

The Berkeley result seems inconsistent with this –but again, I stand to be corrected! They seem to be attempting to “hexagonalize” what otherwise seems to be an octagonal motif.

I might believe in reading the full NATURE PHOTONICS paper that the source of the laser emission that they observe (Fgiure 3, f,g,and h) might actually be the cavity formed by an octagonal arrangement of individual nano-pillars.  Note that their other figures (3 b, c, and d and Figure 4) are simulations. Note that the external laser beam used to excite the nano-structure is one micron in diameter

The laser emission result, however, seems real and could be important to further understanding light interaction with the retina!

Importantly, the  authors propose an internally-reflective helical mechanism underlying laser emission –  that, in my view, could equally result from the octagonal motif of individual nano-pillars as I surmise.

This “rotational motion within the octagonal structure” potentially provides thought for a proposal that I have made that the geometry underlying such a structure seems consisitent with the formation of a mathematical epitrochoid. An epitrochoid, however, derives from “a point on a smaller circle rotating about a larger circle” , i.e., rotational motion. Outside of some light polarization effect I have not been able to see such motion.

The symmetry of the octagonal motif has always fascinated me.

For the quantum physics minded biologist,  I have not previously considered any spatil order  in the many rhodopsin complexes resident in the lateral thylakoid membrane  of receptors. I do remember seeing a paper describing a dimer-like order to these complexes. A sijmple search today finds Nanopillars Photonic Crystal Waveguides” (D. N. Chigrin et al, Progress in Electromagnetic Research Symposium 2004, Pisa, Italy, March 28 – 31) where a dimer-like order of nano-pillars is studied a directional waveguides. This perhaps adds to my thought that there may be a laterally directional function operative within each individual receptor (or nano-pillar).  This may underpin the finding of the Berkeley paper of a helical aspect to the light interaction. I believe that such an interaction would obviously function in the femtosecond (10>-15 sec) time domain and be contained within the cavity formed by the octagonal ring of subwavelength dimensioned retinal receptors

GCH

Ojai,CA

2.09.11

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